The purpose of this double-blind, placebo controlled study is to determine whether Arikace™ is effective in treating chronic lung infections caused by Pseudomonas aeruginosa in Cystic Fibrosis subjects. The study will enroll approximately 300 subjects in clinics in the US, Canada, Europe, Australia and New Zealand. Subjects will be randomized to 590 mg Arikace™ or placebo and will receive treatment for 28 days followed by a 56 day safety follow-up period. The subjects will be required to visit the clinic 8 times (including the Screening visit) over a period of approximately 3 months. No overnight stays at the clinic will be required. At the completion of the TR02-109 protocol, subjects who have consented and meet study safety criteria may enroll in the long-term, open-label, multi-cycle extension study of 590 mg of Arikace™ (under a separate protocol TR02-110).